Awab A Salam Mohamed
EGR 557
Dr. Aukes
April 12, 2022
Parameter ID
The goal of this experiment is to determine the stiffness of a laminate beam based on
the thickness of the material and load at the end point.
The procedure used to collect data goes as follows:
1. Measured the thickness of the materials, 10 mils, and 30 mils
2. Placing a weight to clamp down the material at 13 cm.
3. Hanging various weights at the other end of the material (27g, 54g, 81g, 108g,
135g)
4. Measure distance in z-direction.
After collecting, analyzing, and graphing the data, it was evident that the sample
produced nearly linear results. Thus, I plan on linearizing the data to produce the best fit
line since the data is already producing a line that is very close to the linearized line.
Data collected:
Load(g)
27
54
81
108
135
Change in
Z (inches)
10 mils
0.45
0.675
0.90
1.125
1.25
30 mils
0.27
0.40
0.52
0.65
0.75
Discussion
1. What could you have done better in your experiment design and setup?
Having a fixed ruler or measuring tape on the wall could have increased the accuracy
and consistency of the results. A camera tracking software could have been more
accurate since it eliminates human error.
2. Discuss your rationale for the model you selected. Describe any assumptions or
simplifications this model makes. Include external references used in selecting
or understanding your model.
The model selected will help determine which material thickness is ideal for stiffer links,
especially under load. I collected data for 10 mil and 30 mil fiberglass sheets using
identical weights for both.
The assumptions made are:
○ Other layers do not contribute to stiffness
○ We have a symmetric laminate.
3. Justify the method you selected (least squares, nonlinear least squares,
scipy.optimize.minimize(), Evolutionary algorithm, etc. ) for fitting experimental
data to the model, as well as the specific algorithm used.
The method selected for fitting the experimental data was least square optimization in
order to find a linear relationship between load and link flexibility. The data collected
appear to be nearly linear and least square approximation helped provide useful data.
4. How well does your data fit the model you selected? Provide a numerical value
as well as a qualitative analysis, using your figure to explain.
The data helped us determine that the 30 mil fiberglass sheet is a better material to use
in order to reduce flex in our links. From the data we also determined that the flexibility
is linearly related to the load on the end of the link. The 30 mil sheet flexes at a much
slower rate than the 10 mil sheet. From the data we can find the stiffness of the material
through the following equation:
E being the Young’s modulus of fiberglass, A being the cross sectional area, and L is the
length.
E = 1.6 kPa
A = 0.05*0.001524 = 0.0000762 m^2 (height=two 30 mil sheets for laminate process)
L = 0.130 m
Which ultimately gives us a stiffness (k) of 9.4*10^6 N/m. This value will be used in the
code to have accurate stiffness
Using a two link example code, I was able to determine that the high stiffness value
infact does not cause much flex in the link as intended.
5. What are the limits of your model, within which you are confident of a good fit?
Do you expect your system to operate outside of those limits?
The actual prototype will consist of 5 layers,
while the data is simply for 2 layers of material.
In the case that we assume that the adhesive
and hinge material don’t provide any stiffness.
The fiberglass was also only tested up to 135
grams (1.32N), and while the data shows an
almost linear relationship with the flexibility, it is
not guaranteed with significantly larger weights.
